TY - JOUR
T1 - Characterization of finite type string link invariants of degree <5
AU - Meilhan, Jean Baptiste
AU - Yasuhara, Akira
N1 - Funding Information:
† Supported by a grant from the Heiwa Nakajima Foundation. ‡ Partially supported by a Grant-in-Aid for Scientific Research (C) (#20540065) of the Japan Society for the Promotion of Science.
PY - 2010/5
Y1 - 2010/5
N2 - We give a complete set of finite type string link invariants of degree <5. In addition to Milnor invariants, these include several string link invariants constructed by evaluating knot invariants on certain closures of (cabled) string links. We show that finite type invariants classify string links up to Ck-moves for k≤5, which proves, at low degree, a conjecture due to Goussarov and Habiro. We also give a similar classification of string links up to Ck-moves and concordance for k≤6.
AB - We give a complete set of finite type string link invariants of degree <5. In addition to Milnor invariants, these include several string link invariants constructed by evaluating knot invariants on certain closures of (cabled) string links. We show that finite type invariants classify string links up to Ck-moves for k≤5, which proves, at low degree, a conjecture due to Goussarov and Habiro. We also give a similar classification of string links up to Ck-moves and concordance for k≤6.
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U2 - 10.1017/S0305004110000046
DO - 10.1017/S0305004110000046
M3 - Article
AN - SCOPUS:77952549533
SN - 0305-0041
VL - 148
SP - 439
EP - 472
JO - Mathematical Proceedings of the Cambridge Philosophical Society
JF - Mathematical Proceedings of the Cambridge Philosophical Society
IS - 3
ER -